The present invention relates to an apparatus for separating punched-out workpieces from the surrounding waste material. When punching predetermined shapes for example, to make cartons or the like out of flat material, it is customary not to sever the workpiece shape completely along the entire length of the cut line, but rather to leave lands or bridges at a few locations in order to retain the punched-out workpieces within the plane of the original flat material so that the workpieces may be arranged in a stack. The stacking is usually accomplished in a fully automatic manner. When the stack reaches a predetermined height, the stacked, punched-out material is handled in entire packets to break out the workpieces to separate them from the surrounding waste material. This operation is manually done by means of rubber hammers, air pressure hammers, or milling tools. In spite of the use of these auxiliary means, the severing of the punched-out pieces from the surrounding waste material is rather cumbersome and requires the exertion of a substantial force. Besides, it is time consuming.